The transport equation for the intermittency 
is defined as:
 | (4–169) |
The transition sources are defined as follows:
 | (4–170) |
where 
is the strain rate magnitude, 
is an empirical correlation that controls the length of the transition region,
and 
and 
hold the values of 2 and 1, respectively. The destruction/relaminarization
sources are defined as follows:
 | (4–171) |
where 
is the vorticity magnitude. The transition onset is controlled by the following
functions:
 | (4–172) |
 | (4–173) |
 | (4–174) |
where 
is the wall distance and 
is the critical Reynolds number where the intermittency first starts to
increase in the boundary layer. This occurs upstream of the transition Reynolds number
and the difference between the two must be obtained from an empirical
correlation. Both the 
and 
correlations are functions of 
.
The constants for the intermittency equation are:
 | (4–175) |
The transport equation for the transition momentum thickness Reynolds number 
is
 | (4–176) |
The source term is defined as follows:
 | (4–177) |
 | (4–178) |
 | (4–179) |
 | (4–180) |
The model constants for the 
equation are:
 | (4–181) |
The boundary condition for 
at a wall is zero flux. The boundary condition for 
at an inlet should be calculated from the empirical correlation based on the
inlet turbulence intensity.
The model contains three empirical correlations. 
is the transition onset as observed in experiments. This has been modified from
Menter et al. [433] in order to improve the predictions for
natural transition. It is used in Equation 4–176. 
is the length of the transition zone and is substituted in Equation 4–169. 
is the point where the model is activated in order to match both
and 
, and is used in Equation 4–173. These empirical
correlations are provided by Langtry and Menter [335].
 | (4–182) |
The first empirical correlation is a function of the local turbulence intensity,
:
 | (4–183) |
where 
is the turbulent energy.
The Thwaites’ pressure gradient coefficient 
is defined as
 | (4–184) |
where 
is the acceleration in the streamwise direction.
The modification for separation-induced transition is:
 | (4–185) |
Here, 
is a constant with a value of 2.
The model constants in Equation 4–185 have been adjusted from those of
Menter et al. [433] in order to improve the predictions of separated
flow transition. The main difference is that the constant that controls the relation between
and 
was changed from 2.193, its value for a Blasius boundary layer, to 3.235, the
value at a separation point where the shape factor is 3.5 [433].
The boundary condition for 
at a wall is zero normal flux, while for an inlet, 
is equal to 1.0.
The transition model interacts with the SST turbulence model by modification of the
-equation (Equation 4–101), as follows:
 | (4–186) |
 | (4–187) |
 | (4–188) |
where 
and 
are the original production and destruction terms for the SST model. Note that
the production term in the 
-equation is not modified. The rationale behind the above model formulation is
given in detail in Menter et al. [433].
In order to capture the laminar and transitional boundary layers correctly, the mesh must
have a 
of approximately one. If the 
is too large (that is, > 5), then the transition onset location moves
upstream with increasing 
. It is recommended that you use the bounded second order upwind based
discretization for the mean flow, turbulence and transition equations.
When the Transition SST Model is used together with rough walls, the roughness correlation
must be enabled in the Viscous Model Dialog Box. This
correlation requires the geometric roughness height 
as an input parameter, since, for the transition process from laminar to
turbulent flow, the geometric roughness height is more important than the equivalent sand-grain
roughness height 
. Guidance to determine the appropriate equivalent sand-grain roughness height
(based on the geometric roughness height, shape and distribution of the roughness elements) can
be obtained, for example, from Schlichting and Gersten [578]
and Coleman et al. [117].
The roughness correlation is a modification of the built-in correlation for 
and is defined as:
 | (4–189) |
The new defined 
is then used in the correlations for 
and 
. 
represents the transition momentum thickness Reynolds number. The value
specified for the geometric roughness will apply to all walls. In case a different value is
required for different walls, a user-defined function can be specified. It is important to note
that the function for K is used in the volume (not at the wall). The function therefore must
cover the region of the boundary layer and beyond where it should be applied. As an example,
assume a roughness strip on a flat plate (x-streamwise direction, y wall normal z-spanwise) at
the location 
(m) and a boundary layer thickness in that region of perhaps 
(spanwise extent 
(m)). The following pseudo-code will switch between roughness K0 everywhere
(could be zero) and K1 at the transition strip. The height in the y-direction does not have to
be exactly the boundary layer thickness – it can be much larger – as long as it does
not impact other walls in the vicinity.
 | (4–190) |